%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM022+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:59 AM UTC 2025
% Result : Theorem 0.19s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM022+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:22:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(sdtmndtasgtdt0_type, type, (
% 0.19/0.45 sdtmndtasgtdt0: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(tptp_fun_W2_11_type, type, (
% 0.19/0.45 tptp_fun_W2_11: ( $i * $i ) > $i)).
% 0.19/0.45 tff(xR_type, type, (
% 0.19/0.45 xR: $i)).
% 0.19/0.45 tff(xb_type, type, (
% 0.19/0.45 xb: $i)).
% 0.19/0.45 tff(xc_type, type, (
% 0.19/0.45 xc: $i)).
% 0.19/0.45 tff(aElement0_type, type, (
% 0.19/0.45 aElement0: $i > $o)).
% 0.19/0.45 tff(aReductOfIn0_type, type, (
% 0.19/0.45 aReductOfIn0: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(aNormalFormOfIn0_type, type, (
% 0.19/0.45 aNormalFormOfIn0: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(tptp_fun_W3_10_type, type, (
% 0.19/0.45 tptp_fun_W3_10: ( $i * $i ) > $i)).
% 0.19/0.45 tff(xa_type, type, (
% 0.19/0.45 xa: $i)).
% 0.19/0.45 tff(aRewritingSystem0_type, type, (
% 0.19/0.45 aRewritingSystem0: $i > $o)).
% 0.19/0.45 tff(isTerminating0_type, type, (
% 0.19/0.45 isTerminating0: $i > $o)).
% 0.19/0.45 tff(isLocallyConfluent0_type, type, (
% 0.19/0.45 isLocallyConfluent0: $i > $o)).
% 0.19/0.45 tff(sdtmndtplgtdt0_type, type, (
% 0.19/0.45 sdtmndtplgtdt0: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(tptp_fun_W3_16_type, type, (
% 0.19/0.45 tptp_fun_W3_16: $i)).
% 0.19/0.45 tff(tptp_fun_W2_15_type, type, (
% 0.19/0.45 tptp_fun_W2_15: $i)).
% 0.19/0.45 tff(tptp_fun_W1_14_type, type, (
% 0.19/0.45 tptp_fun_W1_14: $i)).
% 0.19/0.45 tff(tptp_fun_W0_13_type, type, (
% 0.19/0.45 tptp_fun_W0_13: $i)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 (aElement0(xb) <=> aElement0(xb)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(2,axiom,((aElement0(xa) & aElement0(xb)) & aElement0(xc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__731')).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (aElement0(xa) & aElement0(xb)),
% 0.19/0.45 inference(and_elim,[status(thm)],[2])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (aElement0(xb)),
% 0.19/0.45 inference(and_elim,[status(thm)],[3])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (aElement0(xb)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (aRewritingSystem0(xR) <=> aRewritingSystem0(xR)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(7,axiom,(aRewritingSystem0(xR)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__656')).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 (aRewritingSystem0(xR)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))))))))), rewrite(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (^[W0: $i, W1: $i] : refl(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (^[W0: $i, W1: $i] : rewrite(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[14, 12])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1)) <=> (~((~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> (~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) <=> ((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))), rewrite((aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)) <=> (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))), ((((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))), rewrite((((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))), ((((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))), (![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> (((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))), rewrite((((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (^[W0: $i, W1: $i] : rewrite(((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))) <=> (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))) <=> ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.45 tff(23,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mNFRDef')).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.45 tff(26,plain,(
% 0.19/0.45 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[25])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[28, 15])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[29, 10])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (^[W2: $i] : rewrite((~((~(aNormalFormOfIn0(W2, xb, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (![W2: $i] : (~((~(aNormalFormOfIn0(W2, xb, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xb, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xb, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[35, 32])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xb, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xb, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[37, 31])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xb, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 (![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[40, 30, 8, 5])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 ((~((~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))))) <=> (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xb, xR))) | (~((~aNormalFormOfIn0(W2, xb, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xb, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[47, 41])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 (((~(aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xb, xR), xR), tptp_fun_W2_11(xb, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))))) | ((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 ((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (isTerminating0(xR) <=> isTerminating0(xR)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(52,axiom,(isLocallyConfluent0(xR) & isTerminating0(xR)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__656_01')).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (isTerminating0(xR)),
% 0.19/0.47 inference(and_elim,[status(thm)],[52])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 (isTerminating0(xR)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[53, 51])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (^[W0: $i] : refl(((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (^[W0: $i] : rewrite(((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aRewritingSystem0(W0) & isTerminating0(W0)) <=> (~((~aRewritingSystem0(W0)) | (~isTerminating0(W0))))), ((~(aRewritingSystem0(W0) & isTerminating0(W0))) <=> (~(~((~aRewritingSystem0(W0)) | (~isTerminating0(W0))))))), rewrite((~(~((~aRewritingSystem0(W0)) | (~isTerminating0(W0))))) <=> ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)))), ((~(aRewritingSystem0(W0) & isTerminating0(W0))) <=> ((~aRewritingSystem0(W0)) | (~isTerminating0(W0))))), (((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> (((~aRewritingSystem0(W0)) | (~isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))))), rewrite((((~aRewritingSystem0(W0)) | (~isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))), (((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (![W0: $i] : ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0))) <=> ![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (![W0: $i] : ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0))) <=> ![W0: $i] : ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElement0(W1) => ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)) <=> ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))), (![W1: $i] : (aElement0(W1) => ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)) <=> ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))), (((aRewritingSystem0(W0) & isTerminating0(W0)) => ![W1: $i] : (aElement0(W1) => ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0))) <=> ((aRewritingSystem0(W0) & isTerminating0(W0)) => ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0))))), rewrite(((aRewritingSystem0(W0) & isTerminating0(W0)) => ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0))) <=> ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))), (((aRewritingSystem0(W0) & isTerminating0(W0)) => ![W1: $i] : (aElement0(W1) => ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0))) <=> ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (![W0: $i] : ((aRewritingSystem0(W0) & isTerminating0(W0)) => ![W1: $i] : (aElement0(W1) => ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0))) <=> ![W0: $i] : ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.47 tff(65,axiom,(![W0: $i] : ((aRewritingSystem0(W0) & isTerminating0(W0)) => ![W1: $i] : (aElement0(W1) => ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mTermNF')).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (![W0: $i] : ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (![W0: $i] : ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | ?[W2: $i] : aNormalFormOfIn0(W2, W1, W0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.47 tff(68,plain,(
% 0.19/0.47 ![W0: $i] : ((~(aRewritingSystem0(W0) & isTerminating0(W0))) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[67])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 (![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (((~![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))) | ((~aRewritingSystem0(xR)) | (~isTerminating0(xR)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR)))) <=> ((~![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))) | (~aRewritingSystem0(xR)) | (~isTerminating0(xR)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 ((~![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))) | ((~aRewritingSystem0(xR)) | (~isTerminating0(xR)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 ((~![W0: $i] : ((~aRewritingSystem0(W0)) | (~isTerminating0(W0)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, W0), W1, W0)))) | (~aRewritingSystem0(xR)) | (~isTerminating0(xR)) | ![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[73, 70, 8, 54])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 (((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | ((~aElement0(xb)) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR))) <=> ((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | (~aElement0(xb)) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 ((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | ((~aElement0(xb)) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 ((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | (~aElement0(xb)) | aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 5, 74])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 ((~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))) | (~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 ((~((~aNormalFormOfIn0(tptp_fun_W2_11(xb, xR), xb, xR)) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))))) | (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (~((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[80, 50])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))) | aElement0(tptp_fun_W2_11(xb, xR))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (aElement0(tptp_fun_W2_11(xb, xR))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xb, xR), xR)))) | sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[84, 81])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 (^[W0: $i] : refl(((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0))) <=> ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0))) <=> ![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 (^[W0: $i] : trans(monotonicity(rewrite((aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0)) <=> (~((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0))))), ((~(aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))) <=> (~(~((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0))))))), rewrite((~(~((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0))))) <=> ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))), ((~(aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))) <=> ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 (![W0: $i] : (~(aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))) <=> ![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 ((~?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))) <=> (~?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 ((~(((sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc)) => ?[W0: $i] : (((aElement0(W0) & aReductOfIn0(W0, xa, xR)) & sdtmndtasgtdt0(W0, xR, xb)) & ?[W1: $i] : (((aElement0(W1) & aReductOfIn0(W1, xa, xR)) & sdtmndtasgtdt0(W1, xR, xc)) & ?[W2: $i] : (((aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2)) & sdtmndtasgtdt0(W1, xR, W2)) & ?[W3: $i] : ((aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3)) & sdtmndtasgtdt0(xc, xR, W3)))))) => ((sdtmndtasgtdt0(xa, xR, xb) & sdtmndtasgtdt0(xa, xR, xc)) => ?[W0: $i] : ((aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0)) & sdtmndtasgtdt0(xc, xR, W0))))) <=> (~(?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0)) | (~(sdtmndtasgtdt0(xa, xR, xb) & sdtmndtasgtdt0(xa, xR, xc))) | (~((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3)))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(92,axiom,(~(((sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc)) => ?[W0: $i] : (((aElement0(W0) & aReductOfIn0(W0, xa, xR)) & sdtmndtasgtdt0(W0, xR, xb)) & ?[W1: $i] : (((aElement0(W1) & aReductOfIn0(W1, xa, xR)) & sdtmndtasgtdt0(W1, xR, xc)) & ?[W2: $i] : (((aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2)) & sdtmndtasgtdt0(W1, xR, W2)) & ?[W3: $i] : ((aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3)) & sdtmndtasgtdt0(xc, xR, W3)))))) => ((sdtmndtasgtdt0(xa, xR, xb) & sdtmndtasgtdt0(xa, xR, xc)) => ?[W0: $i] : ((aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0)) & sdtmndtasgtdt0(xc, xR, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (~(?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0)) | (~(sdtmndtasgtdt0(xa, xR, xb) & sdtmndtasgtdt0(xa, xR, xc))) | (~((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 (~?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))),
% 0.19/0.48 inference(or_elim,[status(thm)],[93])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 (~?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (~?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[95, 90])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (~?[W0: $i] : (aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[96, 90])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (^[W0: $i] : refl($oeq((~(aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0))), (~(aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(99,plain,(
% 0.19/0.48 ![W0: $i] : (~(aElement0(W0) & sdtmndtasgtdt0(xb, xR, W0) & sdtmndtasgtdt0(xc, xR, W0)))),
% 0.19/0.48 inference(nnf-neg,[status(sab)],[97, 98])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[100, 87])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | ((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xb, xR))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xb, xR))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | ((~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xb, xR))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | (~aElement0(tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xb, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xb, xR)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xb, xR))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[104, 101, 85, 83])).
% 0.19/0.48 tff(106,assumption,(~((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16)))), introduced(assumption)).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))) | sdtmndtasgtdt0(xc, xR, W3!16)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (sdtmndtasgtdt0(xc, xR, W3!16)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))) | sdtmndtasgtdt0(xb, xR, W3!16)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (sdtmndtasgtdt0(xb, xR, W3!16)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | ((~aElement0(W3!16)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16)))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | (~aElement0(W3!16)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | ((~aElement0(W3!16)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | (~aElement0(W3!16)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (~aElement0(W3!16)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[113, 101, 110, 108])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))) | aElement0(W3!16)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 ((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 (((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))) | aNormalFormOfIn0(W3!16, W2!15, xR)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (aNormalFormOfIn0(W3!16, W2!15, xR)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[117, 106])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 ((~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR))))))) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[119, 118, 116])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 (((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))) | ((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 ((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))) | aElement0(W2!15)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (aElement0(W2!15)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[123, 106])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aElement0(W2!15)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aElement0(W2!15)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (((~aRewritingSystem0(xR)) | (~aElement0(W2!15)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aElement0(W2!15)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (^[W2: $i] : rewrite((~((~(aNormalFormOfIn0(W2, W2!15, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (![W2: $i] : (~((~(aNormalFormOfIn0(W2, W2!15, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (((~aRewritingSystem0(xR)) | (~aElement0(W2!15)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W2!15, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(W2!15)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 (((~aRewritingSystem0(xR)) | (~aElement0(W2!15)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W2!15, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aElement0(W2!15)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[129, 126])).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W2!15)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W2!15, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aElement0(W2!15)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W2!15)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W2!15, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aElement0(W2!15)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[131, 125])).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W2!15)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W2!15, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aElement0(W2!15)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 (![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[134, 30, 8, 124])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 (((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 ((~((~((~aElement0(W3!16)) | aNormalFormOfIn0(W3!16, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR))))))))) <=> (~((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(W3!16)) | aNormalFormOfIn0(W3!16, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 (((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(W3!16)) | aNormalFormOfIn0(W3!16, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[138, 136])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(W3!16)) | aNormalFormOfIn0(W3!16, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W2!15, xR) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | (~sdtmndtasgtdt0(W2!15, xR, W2)))) | (~((~aNormalFormOfIn0(W2, W2!15, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W2!15, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(W3!16, W2!15, xR) | (~aElement0(W3!16)) | aReductOfIn0(tptp_fun_W3_10(W3!16, xR), W3!16, xR) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)))) | (~((~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~((~aElement0(W3!16)) | (~sdtmndtasgtdt0(W2!15, xR, W3!16)) | (~![W3: $i] : (~aReductOfIn0(W3, W3!16, xR)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[141, 135, 122])).
% 0.19/0.49 tff(143,plain,((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(144,assumption,(xa = xb), introduced(assumption)).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 (sdtmndtasgtdt0(xa, xR, xc) <=> sdtmndtasgtdt0(xb, xR, xc)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 (sdtmndtasgtdt0(xb, xR, xc) <=> sdtmndtasgtdt0(xa, xR, xc)),
% 0.19/0.49 inference(symmetry,[status(thm)],[145])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 ((~sdtmndtasgtdt0(xb, xR, xc)) <=> (~sdtmndtasgtdt0(xa, xR, xc))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 (aElement0(xc) <=> aElement0(xc)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(149,plain,
% 0.19/0.49 (aElement0(xc)),
% 0.19/0.49 inference(and_elim,[status(thm)],[2])).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 (aElement0(xc)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 (((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 (^[W2: $i] : rewrite((~((~(aNormalFormOfIn0(W2, xc, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (![W2: $i] : (~((~(aNormalFormOfIn0(W2, xc, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xc, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 (((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xc, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[155, 152])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xc, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xc, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[157, 151])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xc, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xc)) | ![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[160, 30, 8, 150])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 (((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(163,plain,
% 0.19/0.49 ((~((~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))))) <=> (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 (((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.49 tff(165,plain,
% 0.19/0.49 (((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[164, 162])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(167,plain,
% 0.19/0.50 ((~![W2: $i] : (~((~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xc, xR))) | (~((~aNormalFormOfIn0(W2, xc, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xc, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.50 tff(168,plain,
% 0.19/0.50 (~((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[167, 161])).
% 0.19/0.50 tff(169,plain,
% 0.19/0.50 (((~(aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_11(xc, xR), xR), tptp_fun_W2_11(xc, xR), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))))) | ((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(170,plain,
% 0.19/0.50 ((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.19/0.50 tff(171,plain,
% 0.19/0.50 (((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | ((~aElement0(xc)) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR))) <=> ((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | (~aElement0(xc)) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(172,plain,
% 0.19/0.50 ((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | ((~aElement0(xc)) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(173,plain,
% 0.19/0.50 ((~![W1: $i] : ((~aElement0(W1)) | aNormalFormOfIn0(tptp_fun_W2_11(W1, xR), W1, xR))) | (~aElement0(xc)) | aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.50 tff(174,plain,
% 0.19/0.50 (aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[173, 150, 74])).
% 0.19/0.50 tff(175,plain,
% 0.19/0.50 ((~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))) | (~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(176,plain,
% 0.19/0.50 ((~((~aNormalFormOfIn0(tptp_fun_W2_11(xc, xR), xc, xR)) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))))) | (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.19/0.50 tff(177,plain,
% 0.19/0.50 (~((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[176, 170])).
% 0.19/0.50 tff(178,plain,
% 0.19/0.50 (((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))) | aElement0(tptp_fun_W2_11(xc, xR))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(179,plain,
% 0.19/0.50 (aElement0(tptp_fun_W2_11(xc, xR))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.19/0.50 tff(180,plain,
% 0.19/0.50 (((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_11(xc, xR), xR)))) | sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(181,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[180, 177])).
% 0.19/0.50 tff(182,plain,
% 0.19/0.50 (((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | ((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(183,plain,
% 0.19/0.50 ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | ((~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(184,plain,
% 0.19/0.50 ((~![W0: $i] : ((~aElement0(W0)) | (~sdtmndtasgtdt0(xb, xR, W0)) | (~sdtmndtasgtdt0(xc, xR, W0)))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR))) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.50 tff(185,plain,
% 0.19/0.50 (~sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[184, 101, 181, 179])).
% 0.19/0.50 tff(186,assumption,(sdtmndtasgtdt0(xb, xR, xc)), introduced(assumption)).
% 0.19/0.50 tff(187,plain,
% 0.19/0.50 (^[W0: $i, W1: $i, W2: $i, W3: $i] : refl((sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(188,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.50 tff(189,plain,
% 0.19/0.50 (^[W0: $i, W1: $i, W2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) <=> (~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> (~(~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), trans(monotonicity(rewrite((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) <=> (~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))), ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) <=> (~(~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))))), rewrite((~(~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))) <=> ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))), ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) <=> ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))), ((sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))))), rewrite((sdtmndtasgtdt0(W0, W1, W3) | ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))), ((sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(190,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[189])).
% 0.19/0.50 tff(191,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(192,plain,
% 0.19/0.50 (^[W0: $i, W1: $i, W2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(rewrite(((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) & aElement0(W3)))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) & aElement0(W3)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)))), rewrite(((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3)) <=> ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(193,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[192])).
% 0.19/0.50 tff(194,axiom,(![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mTCRTrans')).
% 0.19/0.50 tff(195,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.19/0.50 tff(196,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.19/0.50 tff(197,plain,(
% 0.19/0.50 ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[196])).
% 0.19/0.50 tff(198,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.19/0.50 tff(199,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[198, 188])).
% 0.19/0.50 tff(200,plain,
% 0.19/0.50 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xc)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xc)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(201,plain,
% 0.19/0.50 ((sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)) | (~aElement0(tptp_fun_W2_11(xc, xR))) | (~aElement0(xc)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR)))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xc)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(202,plain,
% 0.19/0.50 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)) | (~aElement0(tptp_fun_W2_11(xc, xR))) | (~aElement0(xc)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xc)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[201])).
% 0.19/0.50 tff(203,plain,
% 0.19/0.50 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)) | (~aElement0(tptp_fun_W2_11(xc, xR))) | (~aElement0(xc)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xc)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[202, 200])).
% 0.19/0.50 tff(204,plain,
% 0.19/0.50 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR)) | (~aElement0(tptp_fun_W2_11(xc, xR))) | (~aElement0(xc)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(205,plain,
% 0.19/0.50 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xc)) | (~sdtmndtasgtdt0(xb, xR, xc)) | (~sdtmndtasgtdt0(xc, xR, tptp_fun_W2_11(xc, xR))) | (~aElement0(tptp_fun_W2_11(xc, xR))) | sdtmndtasgtdt0(xb, xR, tptp_fun_W2_11(xc, xR))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.50 tff(206,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[205, 199, 8, 5, 150, 186, 181, 179, 185])).
% 0.19/0.50 tff(207,plain,(~sdtmndtasgtdt0(xb, xR, xc)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(208,plain,
% 0.19/0.50 (~sdtmndtasgtdt0(xa, xR, xc)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[207, 147])).
% 0.19/0.50 tff(209,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xa, xR, xc) <=> sdtmndtasgtdt0(xa, xR, xc)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(210,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xa, xR, xb) & sdtmndtasgtdt0(xa, xR, xc)),
% 0.19/0.50 inference(or_elim,[status(thm)],[93])).
% 0.19/0.50 tff(211,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xa, xR, xc)),
% 0.19/0.50 inference(and_elim,[status(thm)],[210])).
% 0.19/0.50 tff(212,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xa, xR, xc)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[211, 209])).
% 0.19/0.50 tff(213,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[212, 208])).
% 0.19/0.50 tff(214,plain,(~(xa = xb)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(215,plain,
% 0.19/0.50 (aElement0(xa) <=> aElement0(xa)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(216,plain,
% 0.19/0.50 (aElement0(xa)),
% 0.19/0.50 inference(and_elim,[status(thm)],[3])).
% 0.19/0.50 tff(217,plain,
% 0.19/0.50 (aElement0(xa)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.50 tff(218,plain,
% 0.19/0.50 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(219,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[218])).
% 0.19/0.50 tff(220,plain,
% 0.19/0.50 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> (((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))))), rewrite((((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(221,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[220])).
% 0.19/0.50 tff(222,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(223,plain,
% 0.19/0.50 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(224,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[223])).
% 0.19/0.50 tff(225,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mTCRDef')).
% 0.19/0.50 tff(226,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.50 tff(227,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.19/0.50 tff(228,plain,(
% 0.19/0.50 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[227])).
% 0.19/0.50 tff(229,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.19/0.50 tff(230,plain,
% 0.19/0.50 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[229, 219])).
% 0.19/0.50 tff(231,plain,
% 0.19/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xa)) | (~aElement0(xb)) | (sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aRewritingSystem0(xR)) | (~aElement0(xa)) | (~aElement0(xb)) | (sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(232,plain,
% 0.19/0.50 (((sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))) | (~aElement0(xb)) | (~aElement0(xa)) | (~aRewritingSystem0(xR))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xa)) | (~aElement0(xb)) | (sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(233,plain,
% 0.19/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))) | (~aElement0(xb)) | (~aElement0(xa)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xa)) | (~aElement0(xb)) | (sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[232])).
% 0.19/0.50 tff(234,plain,
% 0.19/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))) | (~aElement0(xb)) | (~aElement0(xa)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aRewritingSystem0(xR)) | (~aElement0(xa)) | (~aElement0(xb)) | (sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[233, 231])).
% 0.19/0.50 tff(235,plain,
% 0.19/0.50 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))) | (~aElement0(xb)) | (~aElement0(xa)) | (~aRewritingSystem0(xR)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(236,plain,
% 0.19/0.50 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aRewritingSystem0(xR)) | (~aElement0(xa)) | (~aElement0(xb)) | (sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.19/0.50 tff(237,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[236, 230, 8, 217, 5])).
% 0.19/0.50 tff(238,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xa, xR, xb) <=> sdtmndtasgtdt0(xa, xR, xb)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(239,plain,
% 0.19/0.50 (sdtmndtasgtdt0(xa, xR, xb)),
% 0.19/0.51 inference(and_elim,[status(thm)],[210])).
% 0.19/0.51 tff(240,plain,
% 0.19/0.51 (sdtmndtasgtdt0(xa, xR, xb)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.51 tff(241,plain,
% 0.19/0.51 ((~(sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb)))) | (~sdtmndtasgtdt0(xa, xR, xb)) | ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(242,plain,
% 0.19/0.51 ((~(sdtmndtasgtdt0(xa, xR, xb) <=> ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb)))) | ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.19/0.51 tff(243,plain,
% 0.19/0.51 ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[242, 237])).
% 0.19/0.51 tff(244,plain,
% 0.19/0.51 ((~((xa = xb) | sdtmndtplgtdt0(xa, xR, xb))) | (xa = xb) | sdtmndtplgtdt0(xa, xR, xb)),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(245,plain,
% 0.19/0.51 ((xa = xb) | sdtmndtplgtdt0(xa, xR, xb)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.19/0.51 tff(246,plain,
% 0.19/0.51 (sdtmndtplgtdt0(xa, xR, xb)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[245, 214])).
% 0.19/0.51 tff(247,plain,
% 0.19/0.51 ((((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc))) | (~((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))))) <=> ((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc)) | (~((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(248,plain,
% 0.19/0.51 ((aElement0(W0!13) & aReductOfIn0(W0!13, xa, xR) & sdtmndtasgtdt0(W0!13, xR, xb) & aElement0(W1!14) & aReductOfIn0(W1!14, xa, xR) & sdtmndtasgtdt0(W1!14, xR, xc) & aElement0(W2!15) & sdtmndtasgtdt0(W0!13, xR, W2!15) & sdtmndtasgtdt0(W1!14, xR, W2!15) & aNormalFormOfIn0(W3!16, W2!15, xR) & sdtmndtasgtdt0(xb, xR, W3!16) & sdtmndtasgtdt0(xc, xR, W3!16)) <=> (~((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(249,plain,
% 0.19/0.51 ((~(~((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc))))) <=> ((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(250,plain,
% 0.19/0.51 ((sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc)) <=> (~((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(251,plain,
% 0.19/0.51 ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) <=> (~(~((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.51 tff(252,plain,
% 0.19/0.51 ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) <=> ((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[251, 249])).
% 0.19/0.51 tff(253,plain,
% 0.19/0.51 (((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | (aElement0(W0!13) & aReductOfIn0(W0!13, xa, xR) & sdtmndtasgtdt0(W0!13, xR, xb) & aElement0(W1!14) & aReductOfIn0(W1!14, xa, xR) & sdtmndtasgtdt0(W1!14, xR, xc) & aElement0(W2!15) & sdtmndtasgtdt0(W0!13, xR, W2!15) & sdtmndtasgtdt0(W1!14, xR, W2!15) & aNormalFormOfIn0(W3!16, W2!15, xR) & sdtmndtasgtdt0(xb, xR, W3!16) & sdtmndtasgtdt0(xc, xR, W3!16))) <=> (((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc))) | (~((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[252, 248])).
% 0.19/0.51 tff(254,plain,
% 0.19/0.51 (((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | (aElement0(W0!13) & aReductOfIn0(W0!13, xa, xR) & sdtmndtasgtdt0(W0!13, xR, xb) & aElement0(W1!14) & aReductOfIn0(W1!14, xa, xR) & sdtmndtasgtdt0(W1!14, xR, xc) & aElement0(W2!15) & sdtmndtasgtdt0(W0!13, xR, W2!15) & sdtmndtasgtdt0(W1!14, xR, W2!15) & aNormalFormOfIn0(W3!16, W2!15, xR) & sdtmndtasgtdt0(xb, xR, W3!16) & sdtmndtasgtdt0(xc, xR, W3!16))) <=> ((~sdtmndtplgtdt0(xa, xR, xb)) | (~sdtmndtplgtdt0(xa, xR, xc)) | (~((~aElement0(W0!13)) | (~aReductOfIn0(W0!13, xa, xR)) | (~sdtmndtasgtdt0(W0!13, xR, xb)) | (~aElement0(W1!14)) | (~aReductOfIn0(W1!14, xa, xR)) | (~sdtmndtasgtdt0(W1!14, xR, xc)) | (~aElement0(W2!15)) | (~sdtmndtasgtdt0(W0!13, xR, W2!15)) | (~sdtmndtasgtdt0(W1!14, xR, W2!15)) | (~aNormalFormOfIn0(W3!16, W2!15, xR)) | (~sdtmndtasgtdt0(xb, xR, W3!16)) | (~sdtmndtasgtdt0(xc, xR, W3!16)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[253, 247])).
% 0.19/0.51 tff(255,plain,
% 0.19/0.51 (((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | (aElement0(W0!13) & aReductOfIn0(W0!13, xa, xR) & sdtmndtasgtdt0(W0!13, xR, xb) & (aElement0(W1!14) & aReductOfIn0(W1!14, xa, xR) & sdtmndtasgtdt0(W1!14, xR, xc) & (aElement0(W2!15) & sdtmndtasgtdt0(W0!13, xR, W2!15) & sdtmndtasgtdt0(W1!14, xR, W2!15) & (aNormalFormOfIn0(W3!16, W2!15, xR) & sdtmndtasgtdt0(xb, xR, W3!16) & sdtmndtasgtdt0(xc, xR, W3!16)))))) <=> ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | (aElement0(W0!13) & aReductOfIn0(W0!13, xa, xR) & sdtmndtasgtdt0(W0!13, xR, xb) & aElement0(W1!14) & aReductOfIn0(W1!14, xa, xR) & sdtmndtasgtdt0(W1!14, xR, xc) & aElement0(W2!15) & sdtmndtasgtdt0(W0!13, xR, W2!15) & sdtmndtasgtdt0(W1!14, xR, W2!15) & aNormalFormOfIn0(W3!16, W2!15, xR) & sdtmndtasgtdt0(xb, xR, W3!16) & sdtmndtasgtdt0(xc, xR, W3!16)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(256,plain,
% 0.19/0.51 (((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3)))))) <=> ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(257,plain,
% 0.19/0.51 ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3)))))),
% 0.19/0.51 inference(or_elim,[status(thm)],[93])).
% 0.19/0.51 tff(258,plain,
% 0.19/0.51 ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.19/0.51 tff(259,plain,
% 0.19/0.51 ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[258, 256])).
% 0.19/0.51 tff(260,plain,
% 0.19/0.51 ((~(sdtmndtplgtdt0(xa, xR, xb) & sdtmndtplgtdt0(xa, xR, xc))) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xa, xR) & sdtmndtasgtdt0(W0, xR, xb) & ?[W1: $i] : (aElement0(W1) & aReductOfIn0(W1, xa, xR) & sdtmndtasgtdt0(W1, xR, xc) & ?[W2: $i] : (aElement0(W2) & sdtmndtasgtdt0(W0, xR, W2) & sdtmndtasgtdt0(W1, xR, W2) & ?[W3: $i] : (aNormalFormOfIn0(W3, W2, xR) & sdtmndtasgtdt0(xb, xR, W3) & sdtmndtasgtdt0(xc, xR, W3)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[259, 256])).
% 0.19/0.51 Proof display could not be completed: monotonicity rule is not handled
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------